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Quadratic Formula
Falconer Football
It’s October and high school football is back. The coach challenged our math
class to figure out
what the area of the field is. The coach estimated the dimensions of a football
field in yards^{2}.
There’s only one problem, he decided to give the dimensions to the coach as 4x +
2 yards by 2x + 1
yards. Thus, we must figure out the area in terms of x .
To do this, fill in the football field below with Algebra
Tiles . Make sure that the edge lengths
match up to the tiles in each row or column.
Now, add up the amount of each kind of tile you have. This
should represent the area of the
football field in terms of x.
Area =
Finally, the coach told us that x = 29.5 yards. So what is the actual area in yards^{2}?
Grid Multiplication with Tiles
Let’s see how we can
multiply binomials to obtain trinomials using a new technique.
Example 1:
Consider 2 binomials (2x + 2) and (3x + 1).
Setup: Use algebra tiles and grid worksheet to set up a multiplication grid as follows.
Represents an x^{2}.Represents an x. Represents a 1
Use each tile as a row or a column to multiply. For
example in the first row, first column, you would
get x * x = x^{2}. Then place an
x^{2} tile in the appropriate spot.
Fill in the rest of the chart.
Then, record your findings below.
2._______________Number of x^{2} tiles.
Now write the product
below :
3._______________Number of x tiles.
4._______________Number of 1 tiles.
5.______________________________
Example 2:
Note: Black Tiles represent negatives .
When
multiplying negatives, remember to make the signs agree .
For Example: x * 1 =
x so make sure to use a negative x tile .
Work in groups to fill in the chart
and answer questions.
6. What are the factors ? _______________ and
______________.
7. Fill in the grid on your worksheet.
8. _______________Number of x^{2} tiles.
Now write the
product below:
9. _______________Number of x tiles.
10._______________Number of
1 tiles. 11.______________________________
Example 3:
12. Factors :
______________ and _____________.
13. Fill in the grid.
14. Final product: ______________________
Multiply Trinomials!!!
Example 4:
Fill in the charts the same way we did when we used algebra tiles.
Remember, when multiplying exponents to add the exponents.
Combine like terms by adding the coefficients.
16. Coefficient of x ^{4} terms: _____________.19. Coefficient of x
terms:_____________.
17. Coefficient of x^{3} terms:_____________. 20. Sum of constant
terms:____________.
18. Coefficient of x^{2} terms:_____________.
Use 16.20. to write your final product.
21. ___________________________
Example 5:
22. Fill in the grid.
Combine like terms by adding the coefficients.
23. Coefficient of x^{4} terms: ____________.26. Coefficient of x
terms:_____________.
24. Coefficient of x^{3} terms: ____________.27. Sum of constant
terms:____________.
25. Coefficient of x^{2} terms:_____________.
Use 23.27 to write your final product.
28. ___________________________
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